Studies have found that Kaiser Permanente (an integrated health insurance/care provider—basically a non-governmental equivalent of the NHS in comprehensiveness—that is available in many US states) is more efficient and effective than the NHS for about the same cost.
Kaiser’s effectively an HMO, right? Consumers (i.e. employees evaluating their corporate benefits) hated HMO’s at their peak in the ’90’s so much that the initials became politically toxic.
Cheaper plans with more restrictions could exist more broadly. Consumers don’t want them, politicians make hay on the consumer unhappiness and ban the things that allow the plans to be cheap in the first place.
Kaiser is like the NHS in that it does everything in-house. Kaiser members go to Kaiser doctors, stay at Kaiser hospitals, and get prescriptions fulfilled from Kaiser pharmacies.
I agree on "HMO" being tainted. Kaiser has a good reputation in its territories, as does Intermountain, the other big western US integrated system.
Examples:
* <https://www.bmj.com/content/324/7330/135>
* <https://www.bmj.com/content/327/7426/1257>